Current induced oscillations of a space clamped neuron action potential demonstrates a bifurcation scenario originally encapsulated by the four-dimensional Hodgkin-Huxley equations. These oscillations were subsequently described by the two-dimensional FitzHugh-Nagum Equations in close agreement with the Hodgkin-Huxley theory. It is shown that the FitzHugh-Nagumo equations can to close approximation be reduced to a generalized van der Pol oscillator externally driven by the current. The current functions as an external constant force driving the action potential. As a consequence approximate analytic expressions are derived which predict the bifurcation scenario, the amplitudes of the oscillations (...).
- Source: An Analytic Picture Of Neuron Oscillations, P. E. Phillipson - phillipecolorado.edu, P. Schuster, DOI: 10.1142/S0218127404010151, International Journal Of Bifurcation And Chaos, May 2004
- Contributed by Atin Das - dasatinyahoo.co.in